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        <a href="equivalence-module.html">Module&nbsp;equivalence</a> ::
        Class&nbsp;Equivalence
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<!-- ==================== CLASS DESCRIPTION ==================== -->
<h1 class="epydoc">Class Equivalence</h1><span class="codelink"><a href="equivalence-pysrc.html#Equivalence">source&nbsp;code</a></span><br /><br />
<pre class="base-tree">
object --+
         |
        <strong class="uidshort">Equivalence</strong>
</pre>

<hr />
<p>Representation of a general equivalence relation.</p>
<p>An <a href="equivalence.Equivalence-class.html" class="link">Equivalence</a> instance can be used to maintain a partition of objects
into equivalence sets. Two objects <tt class="rst-docutils literal"><span class="pre">x</span></tt> and <tt class="rst-docutils literal"><span class="pre">y</span></tt> are considered
equivalent either implicitly through a key function or explicitly. For the
implicit case, <tt class="rst-docutils literal"><span class="pre">x</span></tt> and <tt class="rst-docutils literal"><span class="pre">y</span></tt> are equivalent if <tt class="rst-docutils literal"><span class="pre">key(x)</span> <span class="pre">==</span> <span class="pre">key(y)</span></tt> for
some provided function <tt class="rst-docutils literal"><span class="pre">key</span></tt> (by default the identity function <tt class="rst-docutils literal"><span class="pre">lambda</span> <span class="pre">x:x</span></tt>).
For the explicit case, <tt class="rst-docutils literal"><span class="pre">x</span></tt> and <tt class="rst-docutils literal"><span class="pre">y</span></tt> are considered equivalent after a call
to <a href="equivalence.Equivalence-class.html#merge" class="link">merge(x,y)</a>, regardless of their keys.</p>
<p>This class makes sure that the equivalence properties (reflexivity, symmetry,
transitivity) are maintained, provided that <tt class="rst-docutils literal"><span class="pre">key(x)</span></tt> remains fixed for a
given object <tt class="rst-docutils literal"><span class="pre">x</span></tt> (i.e. <tt class="rst-docutils literal"><span class="pre">key</span></tt> is deterministic and does not depend on
mutable state of <tt class="rst-docutils literal"><span class="pre">x</span></tt>).</p><br /><br />

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          <td><span class="summary-sig"><a href="equivalence.Equivalence-class.html#__init__" class="summary-sig-name">__init__</a>(<span class="summary-sig-arg">self</span>,
        <span class="summary-sig-arg">key</span>=<span class="summary-sig-default">None</span>)</span><br />
      Initialize a new equivalence relation.</td>
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            <span class="codelink"><a href="equivalence-pysrc.html#Equivalence.__init__">source&nbsp;code</a></span>
            
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          <td><span class="summary-sig"><a name="update"></a><span class="summary-sig-name">update</span>(<span class="summary-sig-arg">self</span>,
        <span class="summary-sig-arg">*objects</span>)</span><br />
      Update this equivalence with the given objects.</td>
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            <span class="codelink"><a href="equivalence-pysrc.html#Equivalence.update">source&nbsp;code</a></span>
            
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          <td><span class="summary-sig"><a name="merge"></a><span class="summary-sig-name">merge</span>(<span class="summary-sig-arg">self</span>,
        <span class="summary-sig-arg">*objects</span>)</span><br />
      Merge all the given objects into the same equivalence set.</td>
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            <span class="codelink"><a href="equivalence-pysrc.html#Equivalence.merge">source&nbsp;code</a></span>
            
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      <span class="summary-type">bool</span>
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          <td><span class="summary-sig"><a href="equivalence.Equivalence-class.html#are_equivalent" class="summary-sig-name">are_equivalent</a>(<span class="summary-sig-arg">self</span>,
        <span class="summary-sig-arg">*objects</span>)</span><br />
      Checks whether all objects are equivalent.</td>
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            <span class="codelink"><a href="equivalence-pysrc.html#Equivalence.are_equivalent">source&nbsp;code</a></span>
            
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      <span class="summary-type">list of lists</span>
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          <td><span class="summary-sig"><a href="equivalence.Equivalence-class.html#partitions" class="summary-sig-name">partitions</a>(<span class="summary-sig-arg">self</span>,
        <span class="summary-sig-arg">objects</span>=<span class="summary-sig-default">None</span>)</span><br />
      Returns the partitioning of <code class="link">objects</code> into equivalence groups.</td>
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            <span class="codelink"><a href="equivalence-pysrc.html#Equivalence.partitions">source&nbsp;code</a></span>
            
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      <span class="summary-type">set</span>
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          <td><span class="summary-sig"><a name="partition"></a><span class="summary-sig-name">partition</span>(<span class="summary-sig-arg">self</span>,
        <span class="summary-sig-arg">obj</span>)</span><br />
      Return the set of objects in the equivalence that are equivalent to
<code class="link">obj</code>.</td>
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          <td><span class="summary-sig"><a name="partition_key"></a><span class="summary-sig-name">partition_key</span>(<span class="summary-sig-arg">self</span>,
        <span class="summary-sig-arg">obj</span>)</span><br />
      Return the key of the equivalence partition <code class="link">obj</code> belongs to.</td>
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    <p class="indent-wrapped-lines"><b>Inherited from <code>object</code></b>:
      <code>__delattr__</code>,
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      <code>__hash__</code>,
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      <code>__reduce__</code>,
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      <code>__setattr__</code>,
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<a name="__init__"></a>
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  <h3 class="epydoc"><span class="sig"><span class="sig-name">__init__</span>(<span class="sig-arg">self</span>,
        <span class="sig-arg">key</span>=<span class="sig-default">None</span>)</span>
    <br /><em class="fname">(Constructor)</em>
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  </td><td align="right" valign="top"
    ><span class="codelink"><a href="equivalence-pysrc.html#Equivalence.__init__">source&nbsp;code</a></span>&nbsp;
    </td>
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  Initialize a new equivalence relation.
  <dl class="fields">
    <dt>Parameters:</dt>
    <dd><ul class="nomargin-top">
        <li><strong class="pname"><code>key</code></strong> - A callable that takes a single argument and returns its
equivalence key (default: identity function).</li>
    </ul></dd>
    <dt>Overrides:
      object.__init__
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  <h3 class="epydoc"><span class="sig"><span class="sig-name">are_equivalent</span>(<span class="sig-arg">self</span>,
        <span class="sig-arg">*objects</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="equivalence-pysrc.html#Equivalence.are_equivalent">source&nbsp;code</a></span>&nbsp;
    </td>
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  <p>Checks whether all objects are equivalent.</p>
<p>An object doesn't have to be inserted first (through <a href="equivalence.Equivalence-class.html#update" class="link">update</a> or <a href="equivalence.Equivalence-class.html#merge" class="link">merge</a>)
in order to appear as an argument. In this case, its <tt class="rst-docutils literal"><span class="pre">key</span></tt> is used to
determine the partition it would belong if it was inserted.</p>
  <dl class="fields">
    <dt>Returns: bool</dt>
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  <h3 class="epydoc"><span class="sig"><span class="sig-name">partitions</span>(<span class="sig-arg">self</span>,
        <span class="sig-arg">objects</span>=<span class="sig-default">None</span>)</span>
  </h3>
  </td><td align="right" valign="top"
    ><span class="codelink"><a href="equivalence-pysrc.html#Equivalence.partitions">source&nbsp;code</a></span>&nbsp;
    </td>
  </table>
  
  Returns the partitioning of <code class="link">objects</code> into equivalence groups.
  <dl class="fields">
    <dt>Parameters:</dt>
    <dd><ul class="nomargin-top">
        <li><strong class="pname"><code>objects</code></strong> (Iterable or None) - If not None, it must be an iterable of objects to be
partitioned. Otherwise, it defaults to the set of objects already
inserted in the equivalence (through <a href="equivalence.Equivalence-class.html#update" class="link">update</a> and <a href="equivalence.Equivalence-class.html#merge" class="link">merge</a>).</li>
    </ul></dd>
    <dt>Returns: list of lists</dt>
        <dd>A list of partitions, each partition being a list of objects.</dd>
  </dl>
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